Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11719316 | C2 | semidirect |
| 2. C13×#466 | C2 | semidirect |
| 3. #11718818 | C2 | semidirect |
| 4. D8×Dic13 | C2 | semidirect |
| 5. C8×C22⋊D13 | C2 | semidirect |
| 6. C2×#88058 | C2 | semidirect |
| 7. #11718694 | C2 | semidirect |
| 8. D13×#107 | C2 | semidirect |
| 9. #11718535 | C2 | semidirect |
| 10. #11718435 | C2 | semidirect |
| 11. #11718420 | C2 | semidirect |
| 83. C22⋊D13 | D8 | semidirect |
| 96. C8×C13 | #41 | semidirect |
| 105. #466 | D13 | semidirect |
| 193. C13 | #3334 | semidirect |
| 221. C8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719316 | 2 |
| C13×#466 | 2 |
| #11718818 | 2 |
| D8×Dic13 | 2 |
| C8×C22⋊D13 | 2 |
| C2×#88058 | 2 |
| #11718694 | 2 |
| D13×#107 | 2 |
| #11718535 | 2 |
| #11718435 | 2 |
| #11718420 | 2 |
| #3334 | 13 |